sdmobj.m

这是matlab解2阶锥工具包

function quiz = sdmobj(quiz,Xindex,L,R,name)
% SDMPB/SDMOBJ - add term to the linear objective
%
% quiz = sdmobj(quiz,Xindex,L,R,name);
%  
%   adds a term to the linear objective
%   the solver will maximise the real part of the objective
%  
%   <Xindex> specifies the matrix variable
%   <L> specifies the row vector multiplying the variable from the left
%   <R> specifies the column vector multiplying the variable from the right
%       default R=L'
%   if <L='tr'> the objective is the maximisation of : trace(R*X) 
%       default R=1
%   <name> is an optional string that describes the added objective term
%
% SEE ALSO sdmvar, sdmlmi, sdmineq and sdmsol.

%   This file is part of SeDuMi Interface 1.04 (JUL2002)
%   Last update 9th Spetember 2002
%   Copyright (C) 2002 Dimitri Peaucelle & Krysten Taitz
%   LAAS-CNRS, Toulouse, France
% 
%   This program is free software; you can redistribute it and/or modify
%   it under the terms of the GNU General Public License as published by
%   the Free Software Foundation; either version 2 of the License, or
%   (at your option) any later version.
% 
%   This program is distributed in the hope that it will be useful,
%   but WITHOUT ANY WARRANTY; without even the implied warranty of
%   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%   GNU General Public License for more details.
% 
%   You should have received a copy of the GNU General Public License
%   along with this program; if not, write to the Free Software
%   Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
    
  %%% check inputs
  if nargin<3
    error('not enough input arguments');
  elseif nargin>5
    error('too many input arguments');
  elseif ~isa(quiz,'sdmpb')
    error('1st input argument must be a SDMPB object');
  end;      
  %%% check the input <Xindex>
  if ( ~isnumeric(Xindex) | (mod(Xindex,2)~=1 & mod(Xindex,2)~=0) | any(size(Xindex)-[1,1]))
    error('2nd input argument (index of the variable) must be an integer');
  elseif Xindex>quiz.var.nb
    error('2nd input argument (index of the variable) exceeds the number of variables');
  elseif Xindex<=0
    error('2nd input argument (index of the variable) must be strictly positive');
  end;
  % dimensions of the variable
  varm=quiz.var.m(Xindex);
  varM=quiz.var.M(Xindex);
  varrow=quiz.var.row(Xindex);
  varcol=quiz.var.col(Xindex);
  %%% check the inputs <L> and <R>
  % in the case the objective is a trace
  if ischar(L)
    if nargin<4, R=1; elseif isempty(R), R=1;
    elseif ~isnumeric(R)
      error('4th input argument (multiplyer of the trace) must be a matrix');
    end;
    % an option due to an old version of SeDuMi Interface
    if isequal(L,'-tr')     
      L='tr'; R=-R;
    end;
    if isequal(L,'tr')
      if max(size(R))==1
	if ~isequal(varrow,varcol)
	  error('The variable (referenced by 2nd input argument) must be a square matrix');
	else
%	  dimbloc=varM+1-varm;
%          nbrow=sqrt(dimbloc);
%          add=sparse(1,1:(1+nbrow):dimbloc,1)*R;
          add=sparse(1,1:(1+varrow):(varrow*varcol),1)*R;
        end;
      else
	if ~isequal(size(R,2),varrow)
	  error(['3rd input argument (Right multiplier) must have the same' ...
	       'number of columns as the number of rows of the' ...
		' variable']);
        end;
        if ~isequal(size(R,1),varcol)
	  error(['3rd input argument (Right multiplier) must have as many' ...
	       ' rows as the number of columns of the variable']);
        end;
	%  define the objective Tr(R*X)=vec(R.').'*vec(X)
	add=sdmvec(R.').';
      end
%      addconj=conj(add);
    else
      error('3rd input argument must either be a row vector or the strings ''tr''');
    end;    
  % in the case the objective is L*X*R = a scalar 
  else
    % check <L>
    if ~isnumeric(L)
      error(['3rd input argument must either be a row vector or the strings ''tr''']);
    end;
    if ~isequal(min(size(L)),1)
      error('3rd input argument must be a vector');
    elseif length(L)~=varrow;
      error(['3rd input argument must be a vector of length equal to the number of rows' ...
	     ' of the variable']);
    end;    
    % force <L> to be a row vector
    L=sdmvec(L).';
    % check <R>
    if nargin<4, R=[]; end;
    if isempty(R)
      R=L';
      if length(R)~=varcol
	error(['4th input argument must be specified for non square' ...
	       ' variables']);
      end;
    else
      if ~isnumeric(R)
	error(['4th input argument must be a vector']);
      elseif ~isequal(min(size(R)),1)
	error('4th input argument must be a vector');
      elseif length(R)~=varcol
	error(['4rd input argument must be a vector of length equal to the number of columns' ...
	     ' of the variable']);
      end;    
      % force <R> to be a column vector
      R=sdmvec(R);
    end;
    %%% define the objective : L*X*R= (R.' kron L)*vec(X)
    add=kron(R.',L);
  end;	

  %%% append the objective's name
  if nargin<5
    name='';
  elseif ~ischar(name)
    error('5th input argument must be a string identifying the added objective');
  end;  
  quiz.obj.name=[quiz.obj.name,name];

  %%% clear the previous solution if necessary
  quiz = sdmclear(quiz); 

  %%% add the term to the objective
  %%% we remind that vec(X)=struc*y+strucconj*conj(y) 
  %%% where y is the vector of decision variables
  %%% therefore the objective writes as
  %%% real(add*vec(X))=real(add*struc*y+add*strucconj*conj(y)
  %%%                 =real(add*struc*y)+real(conj(add)*strucconj*y)
  %%% add the term that depends on the variable terms (not conjugated)
  struclocal=quiz.var.struc;
  if norm(struclocal(varm:varM,:),1)
    sbt=size(quiz.obj.bt);
    [ii,jj,s]=find(add);
    jj=jj+varm-1;
    quiz.obj.bt=quiz.obj.bt+sparse(ii,jj,s,sbt(1),sbt(2));
  end;
  %%% and those that depend on the conjugate elements of the variable
  struclocal=quiz.var.strucconj;
  if norm(struclocal(varm:varM,:),1)
    sbtc=size(quiz.obj.btconj);
    [ii,jj,s]=find(conj(add));
    jj=jj+varm-1;
    quiz.obj.btconj=quiz.obj.btconj+sparse(ii,jj,s,sbtc(1),sbtc(2));
   end;